Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.3 - Factoring Trinomials Whose Leading Coefficient is Not 1 - Exercise Set - Page 443: 14



Work Step by Step

Factoring by grouping: 1. Multiply the leading coefficient, a, and the constant, c. 2. Find the factors of ac whose sum is b. 3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2. 4. Factor by grouping --- Always start by searching for a GCF.... none (other than 1). 1. $ac=+21$ 2. sum = $-10$ ... factors: $-3$ and $-7$ 3. $3x^{2}-10x+7=(3x^{2}-3x)+(-7x+7)$ 4. ... $=3x(x-1)+(-7)(x-1)$ $=(3x-7)(x-1)$ Check by FOIL$\qquad (3x-7)(x-1) $= $F:\quad 3x^{2}$ $O:\quad -3x$ $I:\quad -7x$ $L:\quad +7$ $(3x-7)(x-1)$ = $3x^{2}-10x+7$
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